Question

giải phương trình
c) x-1/(x-2) + (x+3)/(x-4)= 2/(2-x)(x-4)

Answer 1

\(\dfrac{x-1}{x-2}+\dfrac{x+3}{x-4}=\dfrac{2}{\left(2-x\right)\left(x-4\right)}\)

\(\left(ĐKXĐ:x\ne2;x\ne4\right)\)

\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x-4\right)+\left(x+3\right)\left(x-2\right)}{\left(x-2\right)\left(x-4\right)}=\dfrac{-2}{\left(x-2\right)\left(x-4\right)}\)

\(\Rightarrow x^2-4x-x+4+x^2-2x+3x-6=-2\)

\(\Leftrightarrow2x^2-4x=0\)

\(\Leftrightarrow2x\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\x-2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(tmĐKXĐ\right)\\x=2\left(kotmĐKXĐ\right)\end{matrix}\right.\)